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SSAT Upper Level Math : Right Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Possible Answers:

$40\textup { miles}$

$50\textup { miles}$

$10\textup { miles}$

$30\textup { miles}$

$60\textup { miles}$

Correct answer:

$50\textup { miles}$

Explanation:

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of c=50 .

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Example Question #1 : How To Find The Height Of A Right Triangle

If the hypotenuse of a right triangle is 20, and one of the legs is 12, what is the value of the other leg?

Possible Answers:

Correct answer:

Explanation:

The triangle in this problem is a variation of the 3, 4, 5 right triangle. However, it is 4 times bigger. We know this because $5\cdot4=20$ (the length of the hypotenuse) and $3\cdot4=12$ (the length of one of the legs).

Therefore, the length of the other leg will be equal to:

$4\cdot4=16$

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Example Question #33 : Properties Of Triangles

A given right triangle has a base of length 9cm and a total area of $45cm^{2}$ . What is the height of the right triangle?

Possible Answers:

8cm

9cm

5cm

Not enough information provided

10cm

Correct answer:

10cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

2A=bh

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(45cm^{2})}{9cm}=h$

$\frac{90cm^{2}}{9cm}=h$

10cm=h

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Example Question #34 : Properties Of Triangles

A given right triangle has a base length of 10cm and a total area of $100cm^{2}$ . What is the height of the triangle?

Possible Answers:

Not enough information provided

20cm

5cm

10cm

90cm

Correct answer:

20cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

2A=bh

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(100cm^{2})}{10cm}=h$

$\frac{200cm^{2}}{10cm}=h$

20cm=h

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Example Question #31 : Right Triangles

A given right triangle has a hypotenuse of 30cm and a total area of $200cm^{2}$ . What is the height of the triangle?

Possible Answers:

25cm

10cm

20cm

30.77cm

Not enough information provided

Correct answer:

Not enough information provided

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

However, we have not been given a base or leg length for the right triangle, only the length of the hypotenuse and the area. We therefore do not have enough information to solve for the height .

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Example Question #3 : How To Find The Height Of A Right Triangle

The area of a right triangle is 100m^2 . If the base of the triangle is 25m , what is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=25$

$\text{Area}=100$

$100=\frac{25\times height}{2}$

Now, solve for the height.

$25\times height=200$

height=8

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Example Question #37 : Properties Of Triangles

The area of a right triangle is 45m^2 , and the base is 15m . What is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=15$

$\text{Area}=45$

$45=\frac{15\times height}{2}$

Now, solve for the height.

$15\times height=90$

height=6

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Example Question #2 : How To Find The Height Of A Right Triangle

The area of a right triangle is $50\textup{ in}^2$ . If the base of the triangle is $10\textup{ in}$ , what is the length of the height, in inches?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=10$

$\text{Area}=50$

$50=\frac{10\times height}{2}$

Now, solve for the height.

$10\times height=100$

height=10

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Example Question #1 : How To Find The Area Of A Right Triangle

Right Triangle A has hypotenuse 25 inches and one leg of length 24 inches; Right Triangle B has hypotenuse 15 inches and one leg of length 9 inches; Rectangle C has length 16 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the width of Rectangle C?

Possible Answers:

$14\frac{7}{8} \textrm{ in}$

$17 \frac{1}{4} \textrm{ in}$

$10 \frac{1}{2} \textrm{ in}$

$6 \frac{7}{8} \textrm{ in}$

$8 \frac{5}{8} \textrm{ in}$

Correct answer:

$8 \frac{5}{8} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. In each case, we know the length of one leg and the hypotenuse, so we need to apply the Pythagorean Theorem to find the second leg, then take half the product of the legs:

Right Triangle A:

The length of the second leg is

$\sqrt{25^{2} -24 ^{2}} = \sqrt{625 - 576} = \sqrt{49} = 7$ inches.

The area is

$\frac{1}{2} \times 7 \times 24 = 84$ square inches.

Right Triangle B:

The length of the second leg is

$\sqrt{15^{2} -9 ^{2}} = \sqrt{225 - 81} = \sqrt{144} = 12$ inches.

The area is

$\frac{1}{2} \times 9 \times 12 = 54$ square inches.

The sum of the areas is 84 + 54 = 138 square inches.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $138 \div 16 = 8 \frac{5}{8}$ inches.

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Example Question #2 : How To Find The Area Of A Right Triangle

Right Triangle A has legs of lengths 10 inches and 14 inches; Right Triangle B has legs of length 20 inches and 13 inches; Rectangle C has length 30 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the height of Rectangle C?

Possible Answers:

$10 \textrm{ in}$

$13\frac{1}{3} \textrm{ in}$

Insufficient information is given to determine the height.

$6 \frac{2}{3} \textrm{ in}$

$5 \textrm{ in}$

Correct answer:

$6 \frac{2}{3} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. The area of Right Triangle A is equal to $\frac{1}{2} \times 10 \times 14 = 70$ square inches; that of Right Triangle B is equal to $\frac{1}{2} \times 20 \times 13 = 130$ square inches. The sum of the areas is 70 + 130 = 200 square inches, which is the area of Rectangle C.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $200 \div 30 = 6 \frac{2}{3}$ inches.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Right Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #33 : Properties Of Triangles

Example Question #34 : Properties Of Triangles

Example Question #31 : Right Triangles

Example Question #3 : How To Find The Height Of A Right Triangle

Example Question #37 : Properties Of Triangles

Example Question #2 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Area Of A Right Triangle

Example Question #2 : How To Find The Area Of A Right Triangle

All SSAT Upper Level Math Resources

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